To gain this trophy, you will need to kill all the Sper Mutants. There are 5 in total.
I found the easiest way to kill them, is to use the Fat Man mini nuke, or use the plasma rifle if you have one.
These are the locations where they can be found:
1. Before entering Galaxy News Radio: You will encounter the first behemoth before entering the Galaxy News Radio building. Wait for him to breach though the flipped over truck and then wait for the Behemoth to kill a few of the Brotherhood of Steel Soldiers. The body near the statue will contain the Fat Man mini nuke.
2. Evergreen Mills: The Behemoth is trapped behind an electric fence. First dispose of the Raiders in the area then, go towards the Behemoth but do not open the gate. Instead just keep shooting him though the fence. You can either kill him really fast with the mini nuke, or save your ammo and do it with whatever weapon you have with a good supply of ammo. It will take a while, but you can save yourself another Nuke for later.
3. The Capital Wasteland: Northeast of Evergreen Mills go to the end of the train tracks where there are 3 trains that are knocked over. In the middle of these are two shopping carts. Inside one is a teddy bear. Take the Teddy bear, and the Behemoth will appear shortly after. Reccomended to use a mini nuke on him, as he can easily kill you in 2 hits.
4. The Capitol Bulding: This is located in the heart of Washington D.C. The Behemoth is located in the basement of the building. An easy way of killing him is by staying back behind the door where he does not fit though. He will not be able to attack you making this an easy kill.
5. Takoma Industrial. Takoma is quite far to the east of Galaxy News Radio.He will be in the industrial part, in the backyard area. Reccomended to use a Mini nuke.
I have added a video guide for those who prefer to visually see where all the Behemots are located. All credit for the video goes to Overkill360 on Youtube.